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The Tail Suspension Test
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Tales of Tails.

Christopher Essex1, Bjarne Andresen2

  • 1Department of Mathematics, Middlesex College, The University of Western Ontario, London, ON N6A 5C1, Canada.

Entropy (Basel, Switzerland)
|May 16, 2023
PubMed
Summary
This summary is machine-generated.

For long timescales, fluctuating systems exhibit non-Gaussian distributions, challenging traditional statistical mechanics. These systems lack a global temperature, even with local thermal equilibrium.

Keywords:
effect of tailsprobability density distributionsslow timethermodynamicsvery long timescales

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Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Non-equilibrium Systems

Background:

  • Traditional statistical mechanics assumes Gaussian distributions, where extreme events (tails) are negligible for averages.
  • Long timescale (slow time) regimes and fluctuating local equilibrium systems deviate from this assumption.
  • These systems exhibit non-Gaussian tails, necessitating a re-evaluation of standard thermodynamic concepts.

Purpose of the Study:

  • To investigate the implications of non-Gaussian tail behavior in fluctuating local equilibrium systems.
  • To explain the observational challenges associated with these tail behaviors.
  • To clarify the relationship between time-coarse graining and non-Gaussian distributions.

Main Methods:

  • Analysis of fluctuating local equilibrium systems.
  • Examination of probability density functions (PDFs) and their convolutions.
  • Investigation of the impact of time-coarse graining on distribution tails.

Main Results:

  • Fluctuating local equilibrium systems generate non-Gaussian distributions that do not support a global temperature.
  • Observational challenges arise from the low probability but significant impact of tail behaviors.
  • Time-coarse graining is directly linked to the convolution processes creating non-Gaussian behavior.
  • Truncating the tails of the PDF exacerbates non-Gaussian characteristics.

Conclusions:

  • Standard statistical mechanics is insufficient for describing long-timescale fluctuating systems.
  • The concept of a global temperature is undefined in systems with fluctuating local thermodynamic equilibrium.
  • Understanding non-Gaussian tail behavior is crucial for accurately modeling complex thermodynamic systems.